Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for M24

Name:
M24
Group order:
244823040 = 210 ⋅ 33 ⋅ 5 ⋅ 7 ⋅ 11 ⋅ 23
Number of classes:
26
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,23]
Maximal subgroups:
  Order Index Structure Name
1 10200960 24 M23 M23
2 887040 276 M22.2 M22.2
3 322560 759 24:A8 2^4:a8
4 190080 1288 M12.2 M12.2
5 138240 1771 26:3.S6 2^6:3.s6
6 120960 2024 L3(4).3.22 L3(4).3.2_2
7 64512 3795 26:(L3(2) × S3) 2^6:(psl(3,2)xs3)
8 6072 40320 L2(23) L2(23)
9 168 1457280 L3(2) L3(2)
Stored Sylow p normalizers:
p Order Index Structure Name
2 1024 239085 M24N2 M24N2
3 216 1133440 31+2:D8 3^(1+2):D8
5 240 1020096 (A4 × D10).2 (A4xD10).2
7 126 1943040 7:3 × S3 7:3xS3
11 110 2225664 11:10 11:10
23 253 967680 23:11 23:11
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
11 dec. matrix (PDF)
23 dec. matrix (PDF)
Atlas representations:
67 available
Group constructions in GAP:
AtlasGroup( "M24" ), MathieuGroup( 24 ), PrimitiveGroup( 24, 1 ), PrimitiveGroup( 276, 4 ), PrimitiveGroup( 759, 1 ), PrimitiveGroup( 1288, 2 ), PrimitiveGroup( 1771, 2 ), PrimitiveGroup( 2024, 1 ), PrimitiveGroup( 3795, 1 ), TransitiveGroup( 24, 24680 )
Stored class fusions from this table:
211:M24, J4, 211:M24
Stored class fusions to this table:
2.211:M24, 24:A8, 26:3.S6, 26:31+2.D8, 26:(L3(2) × S3), 211:M24, 212.M24, 22+2+4.(S3 × S3), 22+11+22.(M24 × S3), 23+1+3.L3(2), 3.A6.21, 32.2.S4, 31+2:D8, 7:3 × S3, 11:10, 23:11, (A4 × D10).2, 211.M24, L2(23), L3(2), L3(2) × S3, L3(4).3.22, M12.2, M22.2, M23, M24C2A, 22.24.S5, M24N2, NRS(M24, 2(2+2+4)a), NRS(M24, 24+4), NRS(M24, [29]a), NRS(M24, [29]b), [29].S3a, [29].S3b, 211:M24

File created automatically by GAP on 13-Mar-2024.